Conventionally, “holography” has been known as a technology for displaying a reconstructed image on a reconstructed image display unit, by irradiating an optical wavefront controller unit, in which an optical wavefront control pattern (a hologram) is recorded, with illuminating light.
The “holography” is a technology for reconstructing an optical wavefront itself of an object beam, by controlling at least any one of a phase and an amplitude of the illuminating light by using the optical wavefront control pattern stored in the optical wavefront controller unit.
Additionally, a “simulated annealing” method has been conventionally known as an approximate solution method used for solving a combination optimization problem.
The “simulated annealing” method is a stochastic search technique in which a solution space is searched, and in which an optimum solution is obtained, by repeating an operation (a Move operation) of modifying one solution to another.
In the “simulated annealing” method, in a case where an evaluation value E of a solution is enhanced (that is, in a case where the solution is improved) by a Move operation, this Move operation is adopted, and a solution obtained after the Move operation is set to be a new solution.
On the other hand, in the “simulated annealing” method, in a case where the evaluation value E of the solution is deteriorated (that is, in a case where the solution is worsened) by a Move operation, it is determined whether or not this Move operation is to be adopted (that is, whether or not a solution obtained after the Move operation is to be converted back to the solution prior to the Move operation), on the basis of an adoption probability P (=exp (−ΔE/T)) which is computed on the bases of a parameter value T termed as a “temperature” (hereinafter referred to as a temperature parameter value T) and of an amount ΔE of worsening.
Here, in the “simulated annealing” method, the temperature parameter value T is caused to gradually decrease through an algorithm of the “simulated annealing” method from a sufficiently high temperature to a sufficiently low temperature by taking a sufficiently long time period. Thereby, it is made possible to control the probability of adopting a case of a Move operation worsening the solution, and to prevent an optimum solution from being computed locally.
Recently, in the field of holography, techniques using the “simulated annealing” method for optimization particularly of “kinoform” are proposed, among computer generated holograms (CGHs) which are holograms (optical wavefront control patterns) generated through computations by a computer. The amplitude of the kinoform is supposedly constant, and a phase of the kinoform alone is distributed (for example, refer to Non-patent Document 1).
Furthermore, in order to reduce an amount of computation regarding solution evaluation which needs to be performed a large number of times because of the nature of the “simulated annealing” method, there has also been proposed a method of computing a solution obtained after a Move operation on the basis of difference information with a solution prior to the Move operation (for example, refer to Non-patent Document 2).
By using the above method, an amount of computation regarding evaluation of a reconstructed image is reduced to “O(N)”, the evaluation having conventionally required an amount of computation to be “O(NlogN)” for an image size N (=Nx×Ny). In addition, the amount of computation which is “O(NlogN)” means an amount of computation which is in the order of NlogN, and the amount of computation which is “O(N)” means an amount of computation which is in the order of N.
Non-Patent Document 1
Nobukazu Yoshizawa and Toyohiko Yatagai, “Phase Optimization of a Kinoform by Simulated Annealing,” APPLIED OPTICS Vol. 33 No. 5, pp 863-868, 1994
Non-Patent Document 2
Yen-Wei Chen, Shinichiro Yamauchi, Ning Wang and Zensho Nakao, “A Fast Kinoform Optimization Algorithm Based on Simulated Annealing,” IEICE TRANS. FUNDAMENTALS Vol. E83-A No. 4, pp 774-776, April 2000
However, in a method of computing a solution obtained after each of Move operations on the basis of difference information with a solution prior to the Move operation as in the case of conventional Non-patent Document 2, even if an amount of computation for a solution obtained after each of the individual Move operations can be reduced to the linear order, a fundamental problem that an amount of computation increases with increasing size of a hologram cannot be solved.
In holography using conventional computer generated holograms, computations are performed on the supposition that each equipment performs an ideal behavior in a state where no flaws exist in characteristics of an optical wavefront control device which records a hologram, or in arrangement of the equipment. Accordingly, noise is sometimes recognized in a reconstructed image in a case where the characteristics of the optical wavefront control device are different from those expected, or due to such reasons as minute individual variability existing in actual equipment. As a result, there has been a problem that a reconstructed image which is computed through computer simulation, and a reconstructed image which is reconstructed by incorporating a computer generated hologram into an actual image reconstruction system (an optical system) are not necessarily identical to each other.
Particularly, in a case of holography using the kinoform, the premise is that an amplitude of light on a hologram surface is constant. However, it is not necessarily possible to modulate only a phase of light, and the amplitude of light is also modulated more or less. Thereby, a problem with noise in the reconstructed image is more conspicuous.
The above problems occur as a result of approximately obtaining a computer generated hologram under ideal conditions. Hence, it is considered that reduction of noise in the reconstructed image is possible with more precise computation of the computer generated hologram in consideration of more detailed environmental data and data of each equipment actually used.
However, it is very difficult, and unrealistic, to strictly pursue causes of noise in the reconstructed image, the noise occurring in the real world, and to model elements of noises in a way that the elements are manageable on a computer.